Here is my attempt to define what I mean:
PostureNapoleon's Battles is a grand tactical set of rules however much of the terminology is tactical. A good example of this is unit formations: March Column, Column, Limbered, Line, Unlimbered and Square.
I think of these formations as representing the "posture" of the unit and, along with the facing of the unit, determines what the higher echelon commanders want the unit to do.
March (nee March Column) - move as quickly as possible towards an objective. May even force march. Takes full benefit of roads both for command and crossing terrain. Do not engage the enemy!
Manoeuvre (nee Column and Limbered) - move ready to engage the enemy in long range combat (not artillery), or even go into close range combat if necessary, but realizing it will be a hasty attack.
Deployed (nee Line and Unlimbered) - be prepared to engage enemy in long and close range combat in this location. Movement is limited. [Aside: I would use the new optional rule 12.6 which gives a plus one for a unit in line firing and a minus one for firing on a unit in line. Considering the "line" representing the unit deployed and therefore maximising its fire power as well the defensive characteristics of its location is how I see this optional rule working in a grand tactical sense.]
Defend [against cavalry] (nee Square; "Defend" is the best one word descriptor I have come up with) - infantry be prepared to repulse cavalry. Combat effectiveness and movement is significantly reduced (i.e. cavalry will just bounce off, attacking infantry will be at an advantage and it presents an attractive long range combat target.)
I have never seen the reason for the cavalry line and column formations. Perhaps use the Line combat factor versus cavalry and Column combat factor against infantry in square and artillery. Column movement could be the normal move distance and Line their react move distance.
I would allow an infantry unit in Manoeuvre posture to drop bases to better fit or avoid terrain and for cavalry I would allow them to freely change bases (from single to two or three ranks) as there is no cavalry Deployed posture (unless that is used to represent the cavalry being on react).
Applying this to the question of what factor for infantry to use against a square
Infantry use their column factor (-1) as they are manoeuvering and making a hasty attack. The poor artillery is defending with a -3 and to make things worse the infantry get a +3 for mass. One close combat casualty will eliminate the battery. The Infantry have a 90% chance of dispersing the battery.
Infantry use their VS OT (-3) factor as their posture is defense against cavalry and not suited for attacking. The artillery factor is -3 and the infantry 0 after accounting for mass. A 79% chance for the infantry to disperse the battery, but at a 12% chance to themselves of becoming disordered and having to withdraw (and in what formation would that be?) and a 3% risk of rout (I guess the battery got a few guns turned round and delivered some telling fire - remember close combat ain't all hand to hand).
Infantry use their VS OT factor (-3) as their posture is defense against cavalry, even though the threat is not apparent or may have passed. Attacking infantry use their column factor (-1) as they are manoeuvering and making a hasty attack.
Infantry use their VS OT factor (-3) as their posture is defense against cavalry. Attacking infantry use their LIN factor (2) as they are making a prepared attack.
Both infantry units use their VS OT factors (-3 for the British and -4 for the Nassau) as they are really focused on defending against cavalry. Such combats with heavy negative modifiers may take a while to get a result which is what you'd expect. The posture is not about attacking. The units are still concerned about being attacked by cavalry, even though the immediate threat might have passed.
The infantry use SQ vs CAV (+8) which is what their posture is all about. The cavalry use their LIN factor (+1), but big deal, they are not going to press the attack and will bounce taking no more than one casualty.
The infantry are caught unprepared to defend against cavalry and use their VS OT factor (-3) as do the cavalry (+4). The situation gets interesting if the cavalry is not "attacking" cavalry in which case the infantry would use their COL factor (-1) and the cavalry their LIN factor (+1 in their best years), i.e. their current formation or as I like to imagine it - their posture..
This consideration of posture is also behind my thinking to not use the LIN factor for infantry in column attacking a BUA, a change to Napoleon's Battles brought in with the 4th Edition.
To answer the question about the formation of the withdrawing disordered square, the rules says that it is the current formation and the distance must be at least an inch which would be a problem for most disordered squares except they don't suffer the movement penalty for being disordered or for being in square. I have some issues with unformed movement formation, but will keep them for another post.